Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.leftUnitor_monoidal_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X₁ X₂ : C) {Z : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂ ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.leftUnitor X₁).hom
        (CategoryTheory.MonoidalCategoryStruct.leftUnitor X₂).hom)
      h =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.tensorμ (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X₁
        (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) X₂)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight
          (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorUnit C)).hom
          (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂))
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.leftUnitor (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂)).hom
          h))

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

0 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory